Problem: $A$ $B$ $C$ If: $ AB = 7x + 8$, $ AC = 28$, and $ BC = 7x + 6$, Find $BC$.
Answer: From the diagram, we can see that the total length of ${AC}$ is the sum of ${AB}$ and ${BC}$ $ {AB} + {BC} = {AC}$ Substitute in the expressions that were given for each length: $ {7x + 8} + {7x + 6} = {28}$ Combine like terms: $ 14x + 14 = {28}$ Subtract $14$ from both sides: $ 14x = 14$ Divide both sides by $14$ to find $x$ $ x = 1$ Substitute $1$ for $x$ in the expression that was given for $BC$ $ BC = 7({1}) + 6$ Simplify: $ {BC = 7 + 6}$ Simplify to find ${BC}$ : $ {BC = 13}$